When you hover over a door, a hand icon should appear. When that appears, click and holding down your clicking, drag your finger either forward or backward (depending whether you need to push or pull the door).

If you still have problems, run the game, walk up to that door and then just exit the game.
Once so, could you tell us where you got the game from, and post the hpl.log file.
Since it appears you're on a Macbook, you should be able to find this file at this directory:

One thing you can't do with the touchpad is to right click while holding left click. This is used to throw things. You can use the cmd key to do this instead though. I can imagine it would be difficult to grab and hold things while walking though, as you'll need to keep holding down the touchpad while looking around on it. It's possible, but very tricky. I strongly recommend a USB mouse or something.